Create a function named gaussRule$($f$,$ a$,$ b$,$ c$,$ d$).$ The function takes a bivariate function $f,$ represented as an anonymous function, and the numbers a$,$ b$,$ c$,d,$ defining the rectangle $[a,b][c,d].$ The function should calculate the integral of function $f$ over the given rectangle using the Gauss quadrature rule with three points, as presented in $(3).$

Write a function named nIntegral $($f$,$ ab$,$ cd$,$ k$,$ h$).$ This function, similar to the previous one, takes a two$-$variable function $f$ represented as an anonymous function. Additionally, it takes two two$-$element vectors $ab$ and $cd,$ in which the intervals $a,b$ and $c,d$ are stored, respectively. Furthermore, it takes two natural numbers, $k$ and $h.$ The function should calculate the integral of the function $f$ over the rectangle $[a,b][c,d]$ using a composite Gaussian rule with three points. This means the function should divide the interval $a,b$ into $k$ subintervals and the interval $c,d$ into $h$ subintervals. Then, on each smaller rectangle, apply the rule $(3),$ sum the results, and return an estimate for the integral ${\displaystyle \underset{a}{\overset{b}{}}}{\displaystyle \underset{c}{\overset{d}{}}}f(x,y)dxdy.$

$3$

Let

$f(x,y)=cos((c_1+1)x)sin((c_2+1)y),$

where $c_1$ in $c_2$ are the last two digits of your enrolment number. Plot the graph of function $f(x,y)$ on the rectangle $[0,15][0,20].$ Then numerically compute the integral

${\displaystyle \underset{0}{\overset{20}{}}}{\displaystyle \underset{0}{\overset{15}{}}}f(x,y)dxdy$

using the built in function integral$2.$ On how many subdivisions should we divide the interval $a,b$ and on how many interval $c,d$ so that the composite Gauss rule with three points gives a result that differs by less than ${10}^{-6}$ from the result obtained with the built$-$in function integral$2?$